How does "pussy" come to mean "coward"?

Solution 1:

There is no relation between a woman's genitals and a coward. The meaning of "coward" comes from something else.

Many people think that "pussy" is an diminutive of pusillanimous

pusillanimous

showing a lack of courage or determination; timid.

but a wikipedia article suggests that "pussy" is used as an alternate spelling of an obsolete English word "pursy".

The word pussy can also be used in a derogatory sense to refer to a male who is not considered sufficiently masculine (see Gender role). When used in this sense, it carries the implication of being easily fatigued, weak or cowardly.

According to OED, pussy actually comes from the word puss, a well-used name for cats at that time. It was first used to mean cat.

"cat," 1726, diminutive of puss (n.1), also used of a rabbit (1715). As a term of endearment for a girl or woman, from 1580s (also used of effeminate men). Pussy willow is from 1869, on notion of "soft and furry." To play pussy was World War II RAF slang for "to take advantage of cloud cover, jumping from cloud to cloud to shadow a potential victim or avoid recognition."

Later in the 19th century, it was used as a slang for "female pudenda"

slang for "female pudenda," 1879, but probably older; perhaps from Old Norse puss "pocket, pouch" (cf. Low German puse "vulva"), but perhaps instead from the cat word (see pussy (n.1)) on notion of "soft, warm, furry thing;" cf. French le chat, which also has a double meaning, feline and genital. Earlier uses are difficult to distinguish from pussy (n.1), e.g.: The word pussie is now used of a woman [Philip Stubbes, "The Anatomie of Abuses," 1583] But the use of pussy as a term of endearment argues against the vaginal sense being generally known before late 19c., e.g.: "What do you think, pussy?" said her father to Eva. [Harriet Beecher Stowe, "Uncle Tom's Cabin," 1852] Pussy-whipped first attested 1956.

Solution 2:

OED gives at least two different senses for this word. That of female genitalia is attested as early as 1699, but it's not considered for the sense meaning "coward". The other one, which I copy below, is the purported source of pussy meaning "coward". Basically, using a pet name usually given to women, like sweetheart, princess, etc. to refer to a man mockingly.

a. Chiefly colloq. A girl or woman exhibiting characteristics associated with a cat, esp. sweetness or amiability. Freq. used as a pet name or as a term of endearment. Cf. puss n.1 3, pussycat n. 3.

c1557–65 in T. Wright Songs & Ballads (1860) lxxiv. 209 Adew, my pretty pussy, Yow pynche me very nere.
1583 P. Stubbes Anat. Abuses sig. Hv, You shall haue euery sawcy boy..to catch vp a woman & marie her... So he haue his pretie pussie to huggle withall, it forceth not.
1836 Thackeray Let. 2 July (1945) I. 314 How have you passed the night dear Pussy?
1852 H. B. Stowe Uncle Tom's Cabin I. xvi. 266 ‘What do you think, pussy?’ said her father to Eva.
1932 A. Christie Thirteen Probl. xi. 193 ‘The dame de compagnie, you described, I think, as a pussy, Mrs. Bantry?’ ‘I didn't mean a cat, you know,’ said Mrs. Bantry. ‘It's quite different. Just a big soft white purry person. Always very sweet.’
1941 A. Christie N or M? iii. 38 Old boarding-house pussies. Nothing to do but gossip and knit.
1952 M. Tripp Faith is Windsock iv. 73 ‘Your rear gunner is a hit with the ladies.’ ‘Jake knows how to make the pussies purr; it's an old Jamaican custom.’
[1959 M. Richler Apprenticeship Duddy Kravitz i. ix. 50 Milty ran off crying... ‘What is it, pussy-lamb?’]
1986 D. Potter Singing Detective ii. 45 But tonight there isn't a pussy in sight. Not even a four-legged one. All good people have gone home.


b. slang (chiefly N. Amer.). A sweet or effeminate male; (in later use chiefly) a weakling, a coward, a sissy. Also: a male homosexual.
In quot. 1904: a man likened to a house-cat; a dependent or ‘domesticated’ man.

1904 ‘M. Corelli’ God's Good Man xxi, I shall invite Roxmouth and his tame pussy, Mr. Marius Longford.
1925 S. Lewis Martin Arrowsmith vi. 65 You ought to hear some of the docs that are the sweetest old pussies with their patients—the way they bawl out the nurses.
1934 M. H. Weseen Dict. Amer. Slang 193 Pussy, an effeminate boy.
1958 L. Durrell Mountolive viii. 157 ‘I first met Henry James in a brothel in Algiers. He had a naked houri on each knee.’ ‘Henry James was a pussy, I think.’
1967 ‘iceberg slim’ Pimp v. 103 Look Preston, I got lots of heart. I'm not a pussy. I been to the joint twice. I did tough bits, but I didn't fall apart.
1972 T. O'brien Combat Zone 45 You afraid to be in the war, a goddamn pussy?
1988 J. D. Pistone & R. Woodley Donnie Brasco 119 If he beat me up or cut me, then I would be a pussy in everybody's eyes.
1993 G. Donaldson Ville 20 He believes the only thing worse than being a pussy is being a big pussy.
2004 J. Meno Hairstyles of Damned 125, I..wanted to ask her to Homecoming, but I was a pussy and embarrassed about being in love with her because she was fat.

Solution 3:

I would go with the relationship to pusillanimous, but as a root, and not a reduction.

I was taught in latin long ago that a pusus is one of the seven ages of a male, between infans (non-speaking) and puer (a little being, with a male ending). So someone we would call a toddler.

The root pusillus meaning very small is probably an amplification of pusus, rather than its source, since there is a common diminutive ending being applied.

This makes the word a lot less offensive than we think it is, and it makes the link to cowardice more obvious.